Positive Exponential Function Research Articles

Numerical simulation and investigation of methane gas distribution and extraction in goaf with U-type ventilation of working face

The accumulated methane in goaf during coal mining may leak into the working face under the airflow influence, which is possibly causing disasters such as methane gas excessive at the working face and seriously threatening the mine safety. This paper first established a three-dimensional numerical model of the mining area under U-shaped ventilation, introducing the gas state equation, continuity equation, momentum equation, porosity evolution equation, and permeability evolution equation to simulate the airflow field and gas concentration field in the mining area under the natural state. The reliability of the numerical simulations is then verified by the measured air volumes at the working face. The areas in the mining area where gas is likely to accumulate are also delineated. Subsequently, the gas concentration field in goaf under the gas extraction state was theoretically simulated for different locations of large-diameter borehole. The maximum gas concentration in goaf and the gas concentration trend in the upper corner were analyzed in detail, and the critical borehole location (17.8m from the working face) was determined as the optimum location for gas extraction from the upper corner. Finally, a gas extraction test was carried out on-site to evaluate the application effect. The results show that the measured airflow rate has a small error with the simulated results. The gas concentration in the area without gas extraction is high, with the gas concentration in the upper corner being over 1.2%, which is greater than the critical value of 0.5%. The maximum reduction in gas concentration was 43.9%, effectively reducing the gas concentration in the extraction area after employing a large borehole to extract methane gas. The gas concentration in the upper corner and the distance of the borehole from the working face are expressed as a positive exponential function. The field engineering results show that the implementation of the large borehole at a distance of less than 17.8m from the working face can control the gas in the upper corner to less than 0.5%, effectively reducing the risk of gas in the upper corner. The numerical simulation work in this paper can provide some basic support for the design of an on-site borehole to extract gas from the mining void and reduce the gas hazard in coal mines.

Global stability of critical-speed pulsating fronts for degenerate monostable reactions

This paper is devoted to the global exponential stability of pulsating fronts for a kind of reaction–advection–diffusion equations with degenerate monostable nonlinearity in a periodic medium. We focus on the pulsating front with critical-speed, which is unique up to translation and decays exponentially when it approaches the unstable steady state 0. Based on the sub-super solution and the squeezing methods, we show that the solution will converge to a shift of the front exponentially in time when the general initial data decays faster than a positive exponential function at one end and has a positive lower bound at the other end.

Combining macro and micro experiments to reveal the real-time evolution of permeability of shale

This research analyzed the real-time evolution of shale permeability using a combination of micro and macro experiments. The macro permeability experiment adopted the steady-state method and considered a particular stress path to study the influence of osmotic pressure, pore pressure, and confining pressure on the real-time evolution of permeability. The mechanism of the slippage effect on permeability evolution was studied using microscopic observations. The macro experiment results showed that: (1) permeability decreased as a concave power function with the increase of osmotic pressure; (2) permeability increased as a positive exponential function with an increase in mean pore pressure; (3) permeability decreased as a negative exponential function with an increase in confining pressure; (4) a multiple regression function was established to quantitatively describe the permeability evolution under the combined effect of the confining pressure and pore pressure. Furthermore, increasing the back pressure reduces the osmotic pressure and can effectively weaken the slippage effect, indicating that the back pressure has an essential effect on permeability evolution. The slip and transition flow, which account for a large proportion of all flow patterns, play a significant role in the slippage effect on permeability.

Rapid Growth of Large Forest Fires Drives the Exponential Response of Annual Forest-Fire Area to Aridity in the Western United States.

Annual forest area burned (AFAB) in the western United States (US) has increased as a positive exponential function of rising aridity in recent decades. This non‐linear response has important implications for AFAB in a changing climate, yet the cause of the exponential AFAB‐aridity relationship has not been given rigorous attention. We investigated the exponential AFAB‐aridity relationship in western US forests using a new 1984–2019 database of fire events and 2001–2020 satellite‐based records of daily fire growth. While forest‐fire frequency and duration grow linearly with aridity, the exponential AFAB‐aridity relationship results from the exponential growth rates of individual fires. Larger fires generally have more potential for growth due to more extensive firelines. Thus, forces that promote fire growth, such as aridification, have more potent effects on larger fires. As aridity increases linearly, the potential for growth of large fires accelerates, leading to exponential increases in AFAB.

Wave Propagation Approach for Elastic Transient Responses of Transversely Isotropic Asphalt Pavement under an Impact Load: A Semianalytical Solution

The conventional transfer matrix method, adopted formerly in a semianalytical solution for layered elastic or viscoelastic asphalt pavement structures, has inherent deficiencies, such as ill-condition matrix, numerical overflow, and error accumulation, due to exponential items. This phenomenon is more evident in multilayered dynamic analysis with imperfect interfaces. Moreover, several studies revealed that pavement materials exhibit transverse isotropy in service. Consequently, a novel semianalytical solution methodology, wave propagation approach, was proposed herein to calculate the dynamic responses of asphalt pavement under an impact load considering the transversely isotropic material model and the imperfect interfaces. First, the transfer matrix was established based on matrix theory and wave propagation approach, while the relation between the state vector and wave vector in the transformed domain was constructed simultaneously. Then, combined with the boundary conditions and interface contact conditions, the solution of the wave vector in the transformed domain was derived. Finally, based on Laplace–Hankel inverse transform, the state vector in the time domain was obtained, followed by numerical computation with programming. The accuracy and efficiency of the proposed semianalytical solution, together with the influence regularities of several variables, were discussed. Results showed that due to the absence of positive exponential functions and a large-dimensional matrix, accuracy and efficiency requirements were satisfied during calculation. Moreover, the variation induced by the transversely isotropic properties and interface conditions, presented in the dynamic responses, reiterated that these factors should be considered during the design and analysis of asphalt pavement structures.

Wave propagation approach for dynamic responses of transversely isotropic viscoelastic pavement under impact load

Recently studies reveal that the viscoelasticity of the asphalt layer, the transverse isotropy of each structure layer and the foundation condition of the pavement structure are important factors when analysing the data from falling weight deflectors. However, these factors have not been considered in present analytical solutions simultaneously. To fill this gap, the wave propagation approach was extended to establish a new analytical solution. It was shown that the wave propagation approach could eliminate the positive exponential functions in matrix and only matrix with four elements was adopted in calculation, which contributed to an immense improvement in computational stability and efficiency. A subroutine for transversely isotropic viscoelastic material in finite element software ABAQUS was developed to verify the accuracy of the proposed analytical solution. Several numerical examples were also presented to discuss the influences of the aforementioned factors on the dynamic responses of asphalt pavements.

Investigation on Creep Behavior and Permeability Evolution Characteristics of Sandstone under Different Pore Pressures

To investigate the influence of pore pressure ( σ w ) on the creep behavior and permeability of red sandstone, triaxial creep test with permeability test under different pore pressures was conducted using MTS 815 testing system. The experimental results demonstrate that water has significant weakening effect on the long-term mechanical properties of sandstone, and the long-term strength of sandstone gradually decreases with increase in pore pressures. All permeability-time curves demonstrate a “decreasing-increasing” trend, but two different permeability evolution trends during the steady creep stage are observed, which are related to deviatoric stress. The permeability of both intact ( k 0 ) and fractured sandstone ( k f ) samples increases with the increase in pore pressure, which are in consistent with the failure mode analysis of fractured sandstone samples. However, while the relationship between k 0 and σ w is positive linear, it is a positive exponential function relationship between k f and σ w .

Specificity of the Temperature Dependence of the Gas Combustion Reaction Rates

The main cause of the previously unexplainable most important features of gas-phase combustion was determined. It was shown that the sharp acceleration of combustion during heating and the high rates are primarily caused not by an increase in the rate constant of the limiting step, as was previously believed, but by an increase in the concentration of active intermediate particles with temperature as an exponential function of a positive exponential function of the Boltzmann factor. Such a character of the temperature dependence governs the transition from combustion to explosion and detonation.

Influence of effective stress on gas slippage effect of different rank coals

Gas slippage effect is one of the key factors which would influence gas seepage in coal. The gas permeability of various rank coals under effective stresses are analyzed, and the influence of effective stresses on gas slippage effect of various rank coals and its control mechanism are revealed by the experiment of gas seepage in coal. The results indicate that with the decrease of pore pressure, the gas permeability and the gas slippage effect in coal increases, which follows the variation laws of Klinkenberg slippage equation. The gas slippage effect in various rank coals is controlled by the effective stress, which shows that with the increase of effective stress, the coal permeability decreases and the gas slippage coefficient increases. The relationship between Klinkenberg permeability of coal and its effective stress obeys negative exponential function. With the increase of effective stress, the gas slippage coefficient in coal varies by the positive exponential function. On this basis, a novel evaluation method of gas slippage effect is proposed. The permeability improvement degree of coal is used to quantitatively evaluate the influence degree of gas slippage effect on the coal permeability. With the increase of pore pressure, the permeability improvement degree of different rank coals dropped by the power function. And with the increase of effective stress, the value of permeability improvement degree of coal increases.

Study on the Oxygen Enrichment Effect of Individual Oxygen-Supply Device in a Tunnel of Plateau Mine.

Complex characteristics of the plateau environment such as low oxygen content seriously restrict the exploitation of abundant mineral resources in plateau areas. To regulate the hypoxia environment and improve the comfort of workers engaged in intense physical labor like tunnel excavation operations in plateau mines, an individual oxygen-supply device for tunnel of plateau mine was proposed to create local oxygen enrichment in the area around the human nose. The Computational Fluid Dynamics (CFD) method was used to judge the application’s effect of the individual oxygen-supply device in plateau mine, revealing the oxygen diffusion law under the influence of different oxygen enrichment factors. The orthogonal design and range analysis were used to measure the degree of influence of major factors such as oxygen-supply velocity, oxygen-supply concentration, and tunnel airflow velocity. The results demonstrate that the oxygen mass fraction of the air inhaled by the human had a positive correlation exponential function, a positive correlation linear function, and a negative correlation exponential function, respectively, concerning oxygen-supply velocity, oxygen-supply concentration, and tunnel airflow velocity. The range analysis revealed that the major influencing factors of oxygen enrichment in the tunnel of the plateau mine were, in a descending sequence, as follows: oxygen-supply concentration, tunnel airflow velocity, and oxygen-supply velocity, and the corresponding ranges were 2.86, 2.63, and 1.83, respectively. The individual oxygen-supply device achieved the best oxygen enrichment effect when the oxygen-supply velocity was 5 m/s, the oxygen-supply concentration was 60%, and the tunnel airflow velocity was 0.2 m/s, which increased the oxygen mass fraction of air inhaled by the human to 30.42%. This study has a positive guiding significance for the improvement of the respiration environment in the tunnel of plateau mine.

Laminar flame characteristics of THF family fuels at elevated temperatures and pressures

Laminar flame characteristics of THF family fuels, including tetrahydrofuran (THF), 2-methyltetrahydrofuran (MTHF) and 2,5-dimethyltetrahydrofuran (DMTHF), were studied in constant volume bomb using high-speed schlieren photography technique under the conditions of initial pressure of 1–4 bar, initial temperature of 373–453 K and equivalence ratio of 0.7–1.6. The nonlinear extrapolation method was used to obtain the laminar burning velocity and Markstein length. The results showed that laminar burning velocities of the three fuels vary with equivalence ratio and reached their peak value at equivalence ratio near 1.1, and are accelerated with the elevated initial temperature and decelerated with the elevated initial pressure. The relationship of laminar burning velocity among the three fuels is THF > MTHF > DMTHF. The difference of the velocity is mainly due to the adiabatic flame temperatures and thermal diffusivity which are THF > MTHF > DMTHF and THF≈MTHF > DMTHF respectively. Quantitative analysis indicates that the laminar burning velocity is positive exponential power function with initial temperature and negative exponential power function with initial pressure. The laminar burning velocities of the three fuels are more sensitive to the variation of both initial temperature and pressure for fuel-lean mixtures, and MTHF is the most sensitive among the three fuels. Flame instability among the three fuels is THF≈MTHF > DMTHF, because the relationship of the effective Lewis number and flame thickness is THF < MTHF < DMTHF, meaning that the diffusion-thermal instability among the three fuels is THF > MTHF > DMTHF.

Design of an adaptive dynamic sliding mode control approach for robotic systems via uncertainty estimators with exponential convergence rate

In this work, an adaptive dynamic sliding mode control approach is proposed for robotic systems via uncertainty estimators with exponential convergence rate. The uncertainties are estimated using various uncertainty estimators such as the Fourier series expansion, Legendre polynomials and adaptive fuzzy systems. Also, for each uncertainty estimator, the approximation error is compensated. The adaptation laws are derived using a stability analysis. Moreover, the asymptotic convergence of the tracking error and the boundedness of all closed-loop signals are guaranteed. The novelty of this paper is proposing a positive exponential function for the convergence rate of the adaptation rules to prevent from initial high voltages originated from large initial tracking errors. Another novelty of this paper is presenting a robust control term for the truncation error that improves the accuracy of the control system. Analysis of simulations reveals the effectiveness of the proposed method in terms of fast disturbance rejection and negligible tracking error.

Investigations into the mechanisms of electrohydrodynamic instability in free surface electrospinning

AbstractFree surface electrospinning is a continuous electrospinning method for low-cost, massive production of nanofibers. The interjet distanceλis a critical parameter in free surface electrospinning, which directly determines the nanofiber production efficiency. In this investigation, we studied the interjet distance during free surface electrospinning based on electrohydrodynamic instability theoretically and experimentally, with special interest focused on the effect of surface tension and electric field intensity on the interjet distance. The experimental results indicated that the critical parameters affecting the interjet distance were the surface tension and applied voltage, which was in good compliance with the theoretical prediction. The relationship between interjet distanceλand surface tension followed an allometric law with positive exponential function, and the relationship between interjet distanceλand applied voltage followed an allometric law with negative exponential function. The present results can be used to understand the basic parameters which determine the interjet distance in free surface electrospinning.

A block rational Krylov method for 3-D time-domain marine controlled-source electromagnetic modelling

We introduce a novel block rational Krylov method to accelerate three-dimensional time-domain marine controlled-source electromagnetic modeling with multiple sources. This method approximates the time-varying electric solutions explicitly in terms of matrix exponential functions. A main attraction is that no time stepping is required, while most of the computational costs are concentrated in constructing a rational Krylov basis. We optimize the shift parameters defining the rational Krylov space with a positive exponential weight function, thereby producing smaller approximation errors at later times and reducing iteration numbers. Furthermore, for multi-source modeling problems, we adopt block Krylov techniques to incorporate all source vectors in a single approximation space. The method is tested on two examples: a layered seafloor model and a 3D hydrocarbon reservoir model with seafloor bathymetry. The modeling results are found to agree very well with those from 1D semi-analytic solutions and finite-element time-domain solutions using a backward Euler scheme, respectively. Benchmarks of the block rational Krylov method demonstrate that it can be as up to 10 times faster than backward Euler. The block method also benefits from better memory efficiency, resulting in considerable speedup compared to non-block methods.

Soil Carbon Dioxide Emission: Soil Respiration Measurement in Temperate Grassland, Nepal

Soil carbon dioxide emission: soil respiration is representing a major contributor of accumulating carbon dioxide in the atmosphere that aids to accelerate global warming and altering the climate. Soil temperature, soil water content, sun light and vegetation are considered most common regulators of soil respiration variations in ecosystem. The soil respiration was measured in grassland intended to examine how the soil respiration changed with varying climatic factors, for two years (2015 and 2016) in temperate grassland of Annapurna Conservation Area (ACA), Nepal. In the study, soil temperature accounted exponential function of soil respiration variation at 42.9%, 19.1% and 23.3%, and temperature sensitivity of the soil respiration (Q10) obtained at 6.2, 1.4 and 1.8 in October 2015 and April 2016 and both the measurements were combined, respectively. Significant negative (R2 = 0.50, p < 0.05, October 2015) and positive (R2 = 0.084, p < 0.05, April 2016) exponential function of soil respiration and soil water content were determined, where high soil respiration values were always measured between 30% and 35% of the soil water content. However, linear significant relationship was determined (R2 = 0.376, p < 0.05) between soil respiration and photosynthetic photon flux density (PPFD). Soil respiration value averaged in October 2015 was 357 mg CO2 m-2 h-1 and in April 2016 it was 444.6 mg CO2 m-2 h-1. Above- and below-ground plant biomasses were obtained at 231.1 g d w m-2 and 1538.8 g d w m-2 in October, and at 449.9 g d w m-2 and 349.0 g d w m-2 in April, respectively. This study showed variation of soil respiration in relation to the factors such as soil temperature, soil water content and photosynthetic photon flux density signifying their importance in governing ecosystem function and carbon balance of the temperate grassland ecosystem.

The effect of virtual reality-based balance training on motor learning and postural control in healthy adults: a randomized preliminary study

BackgroundAdults with sedentary lifestyles seem to face a higher risk of falling in their later years. Several causes, such as impairment of strength, coordination, and cognitive function, influence worsening health conditions, including balancing ability. Many modalities can be applied to improve the balance function and prevent falling. Several studies have also recorded the effects of balance training in elderly adults for fall prevention. Accordingly, the aim of this study is to define the effect of virtual reality-based balance training on motor learning and postural control abilities in healthy adults.MethodsFor this study, ten subjects were randomly allocated into either the conventional exercise (CON) or the virtual reality (VR) group. The CON group underwent physical balance training, while the VR group used the virtual reality system 4 weeks. In the VR group, the scores from three game modes were utilized to describe the effect of motor learning and define the learning curves that were derived with the power law function. Wilcoxon Signed Ranks Test was performed to analyze the postural control in five standing tasks, and data were collected with the help of a force plate.ResultsThe average score was used to describe the effect of motor learning by deriving the mathematical models for determining the learning curve. Additionally, the models were classified into two exponential functions that relied on the aim and requirement skills. A negative exponential function was observed in the game mode, which requires the cognitive-motor function. In contrast, a positive exponential function was found in the game with use of only the motor skill. Moreover, this curve and its model were also used to describe the effect of learning in the long term and the ratio of difficulty in each game. In the balance performance, there was a significant decrease in the center of pressure parameters in the VR group, while in the CON group, there was a significant increase in the parameters during some foot placements, especially in the medio-lateral direction.ConclusionThe proposed VR-based training relies on the effect of motor learning in long-term training though different kinds of task training. In postural analysis, both exercise programs are emphasized to improve the balance ability in healthy adults. However, the virtual reality system can promote better outcomes to improve postural control post exercising.Trial registration Retrospectively registered on 25 April 2018. Trial number TCTR20180430005

Species Richness and Distributional Pattern of Amphibians along an Elevational Gradient at Gunung Raya, Pulau Langkawi, Kedah, Malaysia

A study on amphibian community at Gunung Raya, Pulau Langkawi was conducted in order to identify amphibian species richness and species distribution pattern along an elevation gradient. Species richness and distribution pattern of amphibians along an elevational gradient could explain factors that determine ecological processes in a particular highland. Passive sampling method by using two types of traps namely Drift- fenced pitfall trap and PVC pipe trap were used from February 2014 until January 2015. 100 individual comprise of 10 species amphibian were recorded. Leptobrachium smithii were the most abundant (n=37) followed by Megophrys aceras (n=28). Rank abundance curve for amphibian community show a Broken Stick pattern (χ2=12.67, p=0.12). Species accumulation curve does not level off to an asymptote, indicating insufficient sample size despite intensive sampling effort. Estimation analysis by using Chao 1 predictor produces 12 amphibian species based on 100 pooled individuals. A weak positive exponential function fits the distribution pattern of amphibian abundance (y=0.0028x+13.39), reflecting species domination towards the peak. A negative exponential function fits distribution pattern of amphibian species number across the elevation gradient (y=-0.0091x+7.247), due to the lack of permanent water resource at the upper elevation. These results indicated that by understanding the upland ecology of amphibians, important decisions may be critical for designing conservation efforts and planning land use.

Integrating Larval Dispersal, Permitting, and Logistical Factors Within a Validated Habitat Suitability Index for Oyster Restoration

Habitat suitability index (HSI) models are increasingly used to guide ecological restoration. Successful restoration is a byproduct of several factors, including physical and biological processes, as well as permitting and logistical considerations. Rarely are factors from all of these categories included in HSI models, despite their combined relevance to common restoration goals such as population persistence. We developed a Geographic Information System (GIS)-based HSI for restoring persistent high-relief subtidal oyster (Crassostrea virginica) reefs protected from harvest (i.e., sanctuaries) in Pamlico Sound, North Carolina, USA. Expert stakeholder input identified 17 factors to include in the HSI. Factors primarily represented physical (e.g., salinity) and biological (e.g., larval dispersal) processes relevant to oyster restoration, but also included several relevant permitting (e.g., presence of seagrasses) and logistical (e.g., distance to restoration material stockpile sites) considerations. We validated the model with multiple years of oyster density data from existing sanctuaries, and compared HSI output with distributions of oyster reefs from the late 1800’s. Of the 17 factors included in the model, stakeholders identified four factors—salinity, larval export from existing oyster sanctuaries, larval import to existing sanctuaries, and dissolved oxygen—most critical to oyster sanctuary site selection. The HSI model provided a quantitative scale over which a vast water body (~6,000 km2) was narrowed down by 95% to a much smaller suite of optimal (top 1% HSI) and suitable (top 5% HSI) locations for oyster restoration. Optimal and suitable restoration locations were clustered in northeast and southwest Pamlico Sound. Oyster density in existing sanctuaries, normalized for time since reef restoration, was a positive exponential function of HSI, providing validation for the model. Only a small portion (10-20%) of historical reef locations overlapped with current, model-predicted optimal and suitable restoration habitat. We contend that stronger linkages between larval connectivity, landscape ecology, stakeholder engagement and spatial planning within HSI models can provide a more holistic, unified approach to restoration.

Transient Thermal Response of a Multilayered Geomaterial Subjected to a Heat Source

The analysis of layered geomaterials thermo-mechanical coupling response is important in design and analysis of a nuclear waste repository. Conventional analytical approaches usually have some intrinsic faults of ill-conditioned matrices for thick layers or accumulative numerical errors for a great quantity of layers for containing positive exponential functions. This paper presents a stable computational approach with no positive exponential functions to study the transient thermal responses of a layered geomaterial subjected to a heat source. Based on the governing equations of thermo-mechanical coupling problems, the analytical layer elements for a finite layer and a half–space are derived by utilizing Laplace and Hankel transforms. The analytical layer elements are then assembled into the total stiffness matrix and solved in the transformed domain. Finally, the Laplace–Hankel transform inversion is employed to obtain an actual solution in the physical domain. Numerical computations indicate that the difference of geomaterial mass properties between layers shows obvious effects on thermal response of the layered system, and these results can be served as a benchmark solution for future analyses of stratified material.

Microstructure and mechanical properties of hyperuniform heterogeneous materials.

A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.